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Title:
High-precision Leveled Homomorphic Encryption with Batching
Authors: Long Nie, ShaoWen Yao, Jing Liu
Abstract:In most homomorphic encryption schemes based on the RLWE, the native plaintexts are represented as polynomials in a ring Z_t[x]/x^N+1 where t is a plaintext modulus and x^N+1 is a cyclotomic polynomial with degree power of two. An encoding scheme should be used to transform some natural data types(such as integers and rational numbers) into polynomials in the ring. After a homomorphic computation on the polynomial is finished, the decoding procedure is invoked to obtain the result. However, conditions for decoding correctly are strict in a way. For example, the overflows of computation modulo both the plaintext modulus t and the cyclotomic polynomial x^N+1 will result in a unexpected result for decoding. The reason is that decoding the part which is discarded by modular reduction is not 0.
We combine number theory transformation with Hensel Codes to construct a scheme. Intuitively, decoding the discarded part will yield 0 so the limitations are overcome naturally in our scheme. On the other hand, rational numbers can be handled with high precision in parallel.
ePrint: https://eprint.iacr.org/2022/1267
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